# Thread: Need Help with "Exact Values" and absolute value of a linear function.

1. ## Need Help with "Exact Values" and absolute value of a linear function.

1. Don't understand how exact values work
2. |3x-2| = 4 ---- Please solve

2. Originally Posted by liveboon
1. Don't understand how exact values work
2. |3x-2| = 4 ---- Please solve
(1) If the question asks for the exact value of $\displaystyle \frac{2}{\sqrt{2}}$ , you are expected to give the answer in surd form, $\displaystyle \sqrt{2}$ instead of 1.41 because $\displaystyle \sqrt{2}$ is the more exact value to represent the answer than 1.41

(2) $\displaystyle 3x-2=\pm 4$

3. 2.
$\displaystyle |3x - 2| = 4$

Remember that $\displaystyle |3x - 2| = \begin{cases}\phantom{-(}3x-2\phantom{)}\,\textrm{if }3x - 2 \geq 0\\ -(3x - 2)\,\textrm{if }3x - 2 < 0\end{cases}$

$\displaystyle = \begin{cases}3x - 2 \,\textrm{if } x \geq \frac{2}{3}\\ 2 - 3x \,\textrm{if }x < \frac{2}{3}\end{cases}$

So IF $\displaystyle 3x - 2 = 4$ then $\displaystyle x = 2$. Is this possible?

IF $\displaystyle 2 - 3x = 4$ then $\displaystyle x = -\frac{2}{3}$. Is this possible?